Finding Inverse of 3 × 3 Matrix Using Row Operations
To find the inverse of a 3×3 Matrix, you can follow these steps:
Step 1: Start with the given 3×3 Matrix A and create an identity matrix I of the same size, placing A on the left side and I on the right side of an augmented matrix, separated by a line.
Step 2: Apply a series of row operations to the augmented matrix on the left side to transform it into the identity matrix I. The matrix on the right side of the line, which becomes A-1, is the Inverse of the original matrix A.
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Inverse of 3×3 Matrix
Inverse of a 3 × 3 matrix is a matrix which when multiplied by the original Matrix gives the identity matrix as the product. Inverse of a Matrix is a fundamental aspect of linear algebra. This process plays a crucial role in solving systems of linear equations and various mathematical applications. To calculate the inverse, it is required to calculate the adjoint matrix check the matrix’s invertibility by examining its determinant (which should not equal zero), and apply a formula to derive the Inverse Matrix.
This article covers the various concepts of the Inverse of 3 × 3 Matrix and how to Find the Inverse of 3 × 3 Matrix by calculating cofactors, adjoints, and determinants of 3 × 3 Matrix. Later in this article, you will also find solved examples for better understanding, and practice questions are also provided to check what we have learned from this.
Table of Content
- What is the Inverse of 3 × 3 Matrix?
- How to Find the Inverse of 3 × 3 Matrix?
- Elements Used to Find Inverse of 3 × 3 Matrix
- Inverse of 3 × 3 Matrix Formula
- Finding Inverse of 3 × 3 Matrix Using Row Operations
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